hw5 - character present at that leaf Prove the correctness...

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BCB/CprE/ComS 548 Fundamental Algorithms in Computational Biology Fall 2005 Homework 5 Due Thursday, December 8 1. (5 points) Consider the binary character matrix M and phylogenetic tree T shown below. Compute the parsimony score for M on T . 1 2 3 4 5 6 A 0 0 1 1 0 1 B 1 0 1 0 0 1 C 0 0 1 0 0 0 D 1 0 0 1 1 0 E 0 1 0 1 1 0 F 0 1 0 0 1 0 2. (5 points) Note that a most parsimonious phylogeny for a character matrix M need not be bifurcating. Show that, despite this, at least one of the most parsimonious trees for M must be bifurcating. 3. (5 points) Show that a set of non-binary characters may be incompatible even if every pair is compatible. 4. (5 points) Recall that Fitch’s algorithm starts by assigning to each leaf the same state as the
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Unformatted text preview: character present at that leaf. Prove the correctness of the Fitch algorithm by proving the following claim: “After processing an internal node u , the score obtained at u will be the most parsimonious score for the subtree rooted at u ”. 5. (10 points) Let T and T be two phylogenies for the same set of species. Prove that T can be obtained from T by a sequence of NNI operations. Can you give an upper bound on the number of such operations that are needed? (The minimum such number is called the NNI-distance between T and T and is used to measure the closeness between trees.)...
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